Problem: Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{p^2 + 9p}{p^2 - p - 90}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 9p}{p^2 - p - 90} = \dfrac{(p)(p + 9)}{(p - 10)(p + 9)} $ Notice that the term $(p + 9)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 9)$ gives: $y = \dfrac{p}{p - 10}$ Since we divided by $(p + 9)$, $p \neq -9$. $y = \dfrac{p}{p - 10}; \space p \neq -9$